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A and B working together can finish a job in d days. If A [#permalink]
 14 Jul 2007, 18:58
Question Stats:
77% (02:32) correct
22% (02:53) wrong based on 8 sessions
A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d? A. 25 B. 60 C. 15 D. 14 E. 13 Please solve it with your intellectual prowess!
Last edited by Bunuel on 16 Apr 2012, 00:35, edited 2 times in total.
Edited the question and added the OA
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Re: A and B working together can finish a job in d days. If A [#permalink]
16 Apr 2012, 00:36
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Himalayan wrote: A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?
(1) 25
(2) 60
(3) 15
(4) 14
(5) 13
Please solve it with your intellectual prowess! If A works alone and completes the job, he will take d + 5 days --> the rate of A is \frac{1}{d+5} job/day; If B works alone and completes the job, he will take d + 45 days --> the rate of B is \frac{1}{d+45} job/day; Since A and B working together can finish a job in d days, then their combined rate is \frac{1}{d} job/day; So, \frac{1}{d+5}+\frac{1}{d+45}=\frac{1}{d}. At this point it's MUCH better to substitute the values from the answer choices rather than to solve for d. Answer choice C fits: \frac{1}{15+5}+\frac{1}{15+45}=\frac{1}{20}+\frac{1}{60}=\frac{1}{15}. Answer: C.
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Re: A and B working together can finish a job in d days. If A [#permalink]
15 Apr 2012, 18:36
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Himalayan wrote: A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?
(1) 25
(2) 60
(3) 15
(4) 14
(5) 13
Please solve it with your intellectual prowess! 1/(d+5) +1/(d+45)= 1/d => (2d+50)d = (d+5)*(d+45) => d^2 = 9*5*5 => d= 15 hence option C.
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Re: A and B working together can finish a job in d days. If A [#permalink]
15 Apr 2012, 18:29
Sorry to revisit an old post but this was a toughy! Its not a necessary condition that d be an integer.
So working together they can do the job is d days.
Let r_1 be the rate of A
Let r_2 be the rate of B
Working together their rates to do the job is
Equation1:
(r_1+r_2)d=1 (job)
A working alone can do the job by
Equation2:
(r_1)(d+5)=1 (job)
B working alone can do the job by
Equation3:
(r_2)(d+45)=1 (job)
Now set the first equation to the second equation
(r_1+r_2)d=1 = (r_1)(d+5) solve for d to get d=5(r_1/r_2)
Now set equation1 to equation2
(r_1)(d+5)=1 =(r_2)(d+45) solve to get r_1/r_2=(d+45)/(d+5)
Now substitute d=5(r_1/r_2)=5((d+45)/(d+5))
to get d(d+5)=5(d+45)
which leads you to d^2=5*45. Which is equal to d=15 when you square root both sides (of couse d must be positive, were talking about days here!).
Again, tough problem. If anyone has an easier method let us know.
Last edited by alphabeta1234 on 15 Apr 2012, 18:39, edited 1 time in total.
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Re: A and B working together can finish a job in d days. If A [#permalink]
15 Apr 2012, 21:40
Himalayan wrote: A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?
(1) 25
(2) 60
(3) 15
(4) 14
(5) 13
Please solve it with your intellectual prowess! take the total work as X so both A & B can do it in d days, A alone in d+5 and B alone in d+45 rate calculation is total rate = sum of individual rates X/d = X/(d+5) + X/(d+45) we can remove X, then the equation becomes as below 1/d = 1/(d+5) + 1/(d+45) simplification leads to d^2 = 225 d= + or - 15 u cannot have days in negative right as it should take some time to do a task...hence 15 is the answer... Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat 
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Re: A and B working together can finish a job in d days. If A [#permalink]
25 Dec 2012, 21:21
There is always a trick to such Qs when your given A+B= x days , A= x+ something , B=x+ something . To find X , use the formula X=\sqrt{ab} X= \sqrt{5*45}X= 15 days  Answer : [C]
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Re: A and B working together can finish a job in d days. If A [#permalink]
23 Jan 2013, 23:56
thinktank wrote: There is always a trick to such Qs when your given A+B= x days , A= x+ something , B=x+ something . To find X , use the formula X=\sqrt{ab} X= \sqrt{5*45}X= 15 days Answer : [C] What is the source of this trick? good one though.it can reduce the time to ans tremendously
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Re: A and B working together can finish a job in d days. If A [#permalink]
24 Jan 2013, 01:47
I was going through this 9th grade math text book to pick up on my basics, found a number of shortcuts there 
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Re: A and B working together can finish a job in d days. If A [#permalink]
24 Jan 2013, 12:16
1/A = 1/(d+5)
1/B = 1/(d+45)
therefore... 1/(d+5) + 1/(d+45) = 1/d
When you do the math you end up with d^2 = 225. Therefore, d=15
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Re: A and B working together can finish a job in d days. If A [#permalink]
24 Jan 2013, 13:09
 at bunuel..but solving for d is mathematically correct..then why is it that our answer is C
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Re: A and B working together can finish a job in d days. If A [#permalink]
25 Jan 2013, 05:40
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Re: A and B working together can finish a job in d days. If A [#permalink]
25 Jan 2013, 14:41
Ow!wow i now get you..it is still the same whether we solve for d or we plugin the answer choices..the only difference is that plugin method is saving us time:-)
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Re: A and B working together can finish a job in d days. If A
[#permalink]
25 Jan 2013, 14:41
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